Achille’s paradox… why can’t Achilles just reach the tortoise?
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The idea is that to reach the tortoise, Achilles has to cross an infinite number of subdivisions. And since we can’t go across an infinite number of anything, it’s impossible to reach the tortoise.
The fault in the paradox lies in that as the number of subdivisions grow, the length of each decreases. As the number approaches infinity, the length of a given subdivision approaches zero. So ultimately, you get an infinity times zero condition which is mathematically undefined. The paradox is actually a good example of why it’s undefined, as the distance between Achilles and the tortoise can be any finite number.
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